There are several options for you:

• As suggested in the comments, class_weight should boost the loss function towards the preferred class. This option is supported by various estimators, including sklearn.linear_model.LogisticRegression, sklearn.svm.SVC, sklearn.ensemble.RandomForestClassifier, and others. Note there's no theoretical limit to the weight ratio, so even if 1 to 100 isn't strong enough for you, you can go on with 1 to 500, etc.

• You can also select the decision threshold very low during the cross-validation to pick the model that gives highest recall (though possibly low precision). The recall close to 1.0 effectively means false_negatives close to 0.0, which is what to want. For that, use sklearn.model_selection.cross_val_predict and sklearn.metrics.precision_recall_curve functions:

  y_scores = cross_val_predict(classifier, x_train, y_train, cv=3,
                               method="decision_function")
  
  precisions, recalls, thresholds = precision_recall_curve(y_train, y_scores)
  

  If you plot the precisions and recalls against the thresholds, you should see the picture like this:

  

  After picking the best threshold, you can use the raw scores from classifier.decision_function() method for your final classification.

Finally, try not to over-optimize your classifier, because you can easily end up with a trivial const classifier (which is obviously never wrong, but is useless).

As @Maxim mentioned, there are 2 stages to make this kind of tuning: in the model training stage (like custom weights) and the prediction stage (like lowering the decision threshold).

Another tuning for the model-training stage is using a recall scorer. you can use it in your grid-search cross-validation (GridSearchCV) for tuning your classifier with the best hyper-param towards high recall.

GridSearchCV scoring parameter can either accepts the 'recall' string or the function recall_score.

Since you're using a binary classification, both options should work out of the box, and call recall_score with its default values that suits a binary classification:

• average: 'binary' (i.e. one simple recall value)
• pos_label: 1 (like numpy's True value)

Should you need to custom it, you can wrap an existing scorer, or a custom one, with make_scorer, and pass it to the scoring parameter.

For example:

from sklearn.metrics import recall_score, make_scorer

recall_custom_scorer = make_scorer(
    lambda y, y_pred, **kwargs: recall_score(y, y_pred, pos_label='yes')[1]
)

GridSearchCV(estimator=est, param_grid=param_grid, scoring=recall_custom_scorer, ...)